Finite Group Databasebeta

← #16781986

Subgroups — #16781986

Order 3328.

454 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130771C211yesmaximal, characteristic
2#13130705C212yesmaximal
3D13⋊#334C211yesmaximal, characteristic
4#13129715C212yesmaximal
5C8×Q8×D13C211yesmaximal, characteristic
6C4×Q8×D13C2211yescharacteristic
7C2×#88117—22no—
8C2×#88101—21no—
9C2×#88101—21no—
10#11719059C2212yes—
11D13⋊(C4⋊C8)C2212yes—
12C8×Q8×C13C411yescharacteristic, complemented
13Q8×#1055C411yescharacteristic, complemented
14D13×C4⋊C8—21no—
15D13×C4⋊C8C2211yescharacteristic
16#11718491—21no—
17#11718491C411yescharacteristic, complemented
18C4×C8×D13—21no—
19C4×C8×D13C2211yescharacteristic
20C8×Dic26—21no—
21C8×Dic26C411yescharacteristic, complemented
22#11718255—21no—
23#11718253—21no—
24#11718246—22no—
25C2×Q8×D13D411yescharacteristic
26C2×C4⋊#261—22no—
27C2×C4⋊#261—22no—
28C2×C4⋊#261—22no—
29C2×D13⋊C8—22no—
30C4×Q8×C13C2×C411yescharacteristic
31Q8×Dic13Q811yescharacteristic
32C2×C8×D13—21no—
33C2×C8×D13D411yescharacteristic
34C2×C8×D13D411yescharacteristic
35C4⋊C4×D13—21no—
36C4⋊C4×D13D411yescharacteristic
37#88141—21no—
38#88141Q811yescharacteristic
39C42×D13—21no—
40C42×D13C2311yescharacteristic
41C4×Dic26—21no—
42C4×Dic26C2×C411yescharacteristic
43#88117—44no—
44#88112—22no—
45C4⋊#1057—22no—
46#88101—42no—
47#88101—42no—
48C13×C4⋊C8—21no—
49C13×C4⋊C8C2×C411yescharacteristic
50C4×C8×C13—21no—
51C4×C8×C13C2×C411yescharacteristic
52#88054—21no—
53#88054—21no—
54#88054—21no—
55C8×Dic13—21no—
56C8×Dic13—21no—
57C8×Dic13D411yescharacteristic
58C8×Dic13D411yescharacteristic
59C4⋊#1055—21no—
60C4⋊#1055C2×C411yescharacteristic
61C4×#1055—21no—
62C4×#1055C2×C411yescharacteristic
63#8643—131nomaximal, Sylow
64C22×#261—42no—
65C2×Q8×C13C4⋊C411yescharacteristic
66Q8×D13—22no—
67Q8×D13SD1614yes—
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13C2×D411yescharacteristic
71C2×C4×D13C2×D411yescharacteristic
72C2×C4×D13#4111yescharacteristic
73C2×Dic26—21no—
74C2×Dic26C4⋊C411yescharacteristic
75C2×#1057—42no—
76C4⋊#261—42no—
77C4⋊#261—42no—
78C4⋊#261—42no—
79C4⋊#261—42no—
80C4⋊#261—82no—
81D13⋊C8—42no—
82D13⋊C8—42no—
83C2×C8×C13—21no—
84C2×C8×C13C22⋊C411yescharacteristic
85C2×C8×C13C22⋊C411yescharacteristic
86C13×C4⋊C4—21no—
87C13×C4⋊C4C4⋊C411yescharacteristic
88C42×C13—21no—
89C42×C13C22×C411yescharacteristic
90C4⋊Dic13—21no—
91C4⋊Dic13C4⋊C411yescharacteristic
92#6101—21no—
93#6101—21no—
94#6101—21no—
95C4×Dic13—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13C2×D411yescharacteristic
99C4×Dic13C2×Q811yescharacteristic
100C4×Dic13#4111yescharacteristic
101C2×#1055—21no—
102C2×#1055C22⋊C411yescharacteristic
103C2×#1055C22⋊C411yescharacteristic
104C8×D13—21no—
105C8×D13—21no—
106C8×D13—41no—
107C8×D13—41no—
108C8×D13SD1612yes—
109C8×D13Q1612yes—
110C2×C8×Q8—131no—
111#1844—131no—
112#1803—132no—
113C2×#334—131no—
114#1296—132no—
115C22×D13#12111yescharacteristic
116C2×#261—82no—
117C2×#261—82no—
118C2×#261—82no—
119Q8×C13—21no—
120Q8×C13#10612yescomplemented
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13C2×C22⋊C411yescharacteristic
124C2×C4×C13C2×C4⋊C411yescharacteristic
125C2×C4×C13#11711yescharacteristic
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13#12111yescharacteristic
129C2×Dic13C22⋊Q811yescharacteristic
130C2×Dic13C22⋊Q811yescharacteristic
131C4×D13—24no—
132C4×D13—22no—
133C4×D13—42no—
134C4×D13C2×SD1612yes—
135C4×D13C2×SD1611yescharacteristic
136C4×D13C2×Q1611yescharacteristic
137C4×D13#13512yes—
138C4×D13AGL(1,ℤ/8)11yescharacteristic
139C4×D13#13711yescharacteristic
140Dic26—21no—
141Dic26—24no—
142Dic26#10612yescomplemented
143#1057—82no—
144C8×C13—21no—
145C8×C13—41no—
146C8×C13#10312yescomplemented
147#1055—21no—
148#1055—41no—
149#1055#10312yescomplemented
150C2×C4×Q8—131no—
151C8×Q8—131no—
152C8×Q8—131no—
153C8×Q8—131no—
154C8×Q8—261no—
155C8×Q8—261no—
156C8×Q8#26111yescharacteristic, complemented
157C2×#106—261no—
158C2×#106—261no—
159C2×C4⋊C8—131no—
160C2×C4⋊C8—132no—
161C2×C4⋊C8—261no—
162C2×#103—262no—
163C2×C4×C8—131no—
164C2×C4×C8—261no—
165#384—132no—
166#340—262no—
167#334—261no—
168#334—261no—
169C22×C13#38011yescharacteristic
170C2×D13#46011yescharacteristic
171C2×D13#46211yescharacteristic
172C2×D13#46512yes—
173C2×D13#47112yes—
174#261—162no—
175C4×C13—22no—
176C4×C13—21no—
177C4×C13—41no—
178C4×C13C2×#10311yescharacteristic
179C4×C13#41711yescharacteristic
180C4×C13C2×#10611yescharacteristic
181C4×C13#42711yescharacteristic
182Dic13—22no—
183Dic13—21no—
184Dic13—41no—
185Dic13#46512yes—
186Dic13#47511yescharacteristic
187Dic13#47711yescharacteristic
188C22×Q8—131no—
189C22×C8—131no—
190C22×C8—131no—
191C22×C8—261no—
192C22×C8—262no—
193C4×Q8—131no—
194C4×Q8—131no—
195C4×Q8—131no—
196C4×Q8—261no—
197C4×Q8—261no—
198C4×Q8C2×#26111yescharacteristic
199C2×C4⋊C4—131no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—262no—
202C2×C4⋊C4—262no—
203C2×C4⋊C4—262no—
204C2×C42—131no—
205C2×C42—261no—
206#106—522no—
207#106—522no—
208C4⋊C8—21no—
209C4⋊C8—131no—
210C4⋊C8—261no—
211C4⋊C8—261no—
212C4⋊C8—262no—
213C4⋊C8—262no—
214C4⋊C8—261no—
215C4⋊C8—261no—
216C4⋊C8C2×#26111yescharacteristic
217#103—524no—
218C4×C8—21no—
219C4×C8—131no—
220C4×C8—131no—
221C4×C8—131no—
222C4×C8—261no—
223C4×C8—261no—
224C4×C8—261no—
225C4×C8C2×#26111yescharacteristic
226C2×C13#180311yescharacteristic
227C2×C13#180711yescharacteristic
228C2×C13#181511yescharacteristic
229D13#166612yes—
230D13#167212yes—
231C2×Q8—134no—
232C2×Q8—131no—
233C2×Q8—261no—
234C2×Q8—262no—
235C2×Q8C4⋊#26111yescharacteristic
236C22×C4—131no—
237C22×C4—131no—
238C22×C4—131no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4—522no—
242C2×C8—21no—
243C2×C8—131no—
244C2×C8—132no—
245C2×C8—132no—
246C2×C8—131no—
247C2×C8—261no—
248C2×C8—261no—
249C2×C8—261no—
250C2×C8—521no—
251C2×C8—521no—
252C2×C8—522no—
253C2×C8—522no—
254C2×C8—522no—
255C2×C8C22⋊#26111yescharacteristic
256C2×C8C22⋊#26111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—131no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—522no—
264C4⋊C4—522no—
265C4⋊C4—522no—
266C4⋊C4—522no—
267C4⋊C4—1042no—
268C4⋊C4C4⋊#26111yescharacteristic
269C42—21no—
270C42—131no—
271C42—131no—
272C42—131no—
273C42—261no—
274C42—261no—
275C42—261no—
276C42C22×#26111yescharacteristic
277C13#864311yescharacteristic, complemented, Sylow
278C23—131no—
279Q8—21no—
280Q8—132no—
281Q8—264no—
282Q8—261no—
283Q8#8810112yescomplemented
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—131no—
287C2×C4—131no—
288C2×C4—132no—
289C2×C4—132no—
290C2×C4—131no—
291C2×C4—131no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—131no—
295C2×C4—262no—
296C2×C4—264no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—522no—
300C2×C4—1042no—
301C2×C4—1042no—
302C2×C4—1042no—
303C2×C4C2×C4⋊#26111yescharacteristic
304C2×C4#8823711yescharacteristic
305C2×C4C2×C22⋊#26111yescharacteristic
306C8—21no—
307C8—41no—
308C8—132no—
309C8—261no—
310C8—521no—
311C8—1042no—
312C8#8811712yescomplemented
313C22—131no—
314C22—131no—
315C22—132no—
316C22—132no—
317C22#1171913611yescharacteristic
318C4—22no—
319C4—21no—
320C4—41no—
321C4—131no—
322C4—131no—
323C4—132no—
324C4—262no—
325C4—261no—
326C4—521no—
327C4—2082no—
328C4C2×#8810111yescharacteristic
329C4#1171909211yescharacteristic
330C4C2×#8811711yescharacteristic
331C4#1171916411yescharacteristic
332C2—132no—
333C2—132no—
334C2#1313070511yescharacteristic
335C2#1313071211yescharacteristic
336C2#1313072411yescharacteristic
subgroupG/H
centerC22#11719136
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC8×Q8×C13C4
socleC22×C13#380
prime radicalC22×D13#121
cosocleC42×D13C23
hypercenterC8×Q8#261
hypocenterC13#8643
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
12. C8×Q8×C13C4semidirect
13. Q8×#1055C4semidirect
17. #11718491C4semidirect
21. C8×Dic26C4semidirect
120. Q8×C13#106semidirect
142. Dic26#106semidirect
146. C8×C13#103semidirect
149. #1055#103semidirect
156. C8×Q8#261semidirect
277. C13#8643semidirect
283. Q8#88101semidirect
312. C8#88117semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131307712
#131307052
D13⋊#3342
#131297152
C8×Q8×D132
#864313